Methods are awesome~~~

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Australian Education Academy Pty Ltd

2006

MATHEMATICAL METHODS

UNIT 3 & 4

TRIAL EXAMINATION 1 (Solutions)

Published by Australian Education Academy Pty Ltd

ABN: 18 104 474 893

292 Mount Alexander Road, Ascot Vale. 3032

Ph: (03) 9370 0666 Fax: (03) 9375 7277

Email: wendy@aust-education.com.au

SOLUTIONS

Question 1.

a.

[pic]

(4 marks)

b.

[pic]

[pic]

Standard deviation [pic][pic]

(4 marks)

c.

[pic]

(2 marks)

Total 10 marks

Question 2.

(a)

X-height of males

[pic]

[pic]

(3 marks)

b.

[pic]and

[pic]

([pic] A and B are independent)

(3 marks)

Total 6 marks

Question 3.

a.

[pic]

maximum and minimum values of C(t)

are given by

[pic]

(3 marks)

b.

[pic]

(3 marks)

Total 6 marks

Question 4.

a.

[pic]is one-to-one within the domain [2,().

(2 marks)

b.

The range of f is [1,().

(2 marks)

c.

[pic]

(4 marks)

d.

[pic]

Now change x by y

(Inverse function of f is [pic]

(3 marks)

Total 11 marks

Question 5

a.

Since[pic] passes through the point [pic] we have

[pic]

(3 marks)

b. [pic]

(4 marks)

c.

[pic]

(4 marks)

Total 11 marks

Question 6.

Gradient of the left most line segment is

[pic]

Gradient of the middle line segment is 0.

Hence the equation of the derivative curve is y=0 for [pic].

Equation of the parabola is [pic]

( The equation of the derivative curve is [pic].

Derivative does not exists at the points –6, 0, 2 and 6.

[pic]

(4 marks)

b.

Domain of the derivative function is [pic]

(2 marks)

Total 6 marks

Question 7.

(a)

Intersection points are given by

[pic]

(3 marks)...